We analyse various flow coefficients of anisotropic momentum distribution of final state particles in mid-central ($b$ $=$ 5--9 $fm$) Au + Au collisions in the beam energy range $rm E_{rm Lab}$ $=$ $1A -158A$ GeV. Different variants of the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model, namely the pure transport (cascade) mode and the hybrid mode, are employed for this investigation. In the hybrid UrQMD model, the ideal hydrodynamical evolution is integrated with the pure transport calculation for description of the evolution of the fireball. We opt for the different available equations of state (EoS) replicating the hadronic as well as partonic degrees of freedom together with possible phase transitions, viz. hadron gas, chiral + deconfinement EoS and bag model EoS, to investigate their effect on the properties of the final state particles. We also attempt to gain insights about the dynamics of the medium by studying different features of particle production such as particle ratios and net-proton rapidity distribution. The results and conclusions drawn here would be useful to understand the response of various observables to the underlying physics of the model as well as to make comparisons with the upcoming measurements of the future experiments at Facility for Antiproton and Ion Research (FAIR) and Nuclotron-based Ion Collider fAcility (NICA).
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